1980 AHSME Problem 25

In the non-decreasing sequence of odd integers \{a_1,a_2,a_3,\ldots \}=\{1,3,3,3,5,5,5,5,5,\ldots \} each odd positive integer k appears k times. It is a fact that there are integers b, c, and d such that for all positive integers n, a_n=b\lfloor \sqrt{n+c} \rfloor +d, where \lfloor x \rfloor denotes the largest integer not exceeding x. The sum b+c+d equals

\text{(A)} \ 0 \qquad \text{(B)} \ 1 \qquad \text{(C)} \ 2 \qquad \text{(D)} \ 3 \qquad \text{(E)} \ 4

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.